数论与代数的计算导论
A Computational Introduction to Number Theory and Algebra
Victor Shoup · 初版 2005 年
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数论和代数在计算与通信领域扮演着越来越重要的角色，这在它们对密码学和编码理论等领域的引人注目的应用中得到了充分体现。这本入门级著作侧重于算法和应用（例如密码学与纠错码），面向广泛的受众。其对数学前置要求极低：除了典型的本科微积分课程内容和少许证明经验外，不预设其他知识——其余内容均从零开始推导。因此，本书能够满足多种需求
Hacker News 上怎么说
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……收获很大。很多题我都不会做，但光看题目陈述通常就足以让我意识到自己没弄懂某些概念。刚开始学密码学（crypto）时，我花了很多时间读 Shoup 的另一本免费高质量好书《A Computational Introduction to Number Theory and Algebra》[1]。我刷了很多练习题，甚至还纠正了书里的几处结果，一度还想出一本习题解答手册。我给教授发了邮件……
…rewarding. I can't do many of them, but reading the problem statements is usually enough to make me realize I don't understand something. When I started learning crypto, I spent a lot of time reading A Computational Introduction to Number Theory and Algebra [1] another free, high-quality book by Shoup. I did a lot of exercises, even corrected some results in the book, and at one point thought that I wanted to publish a solution manual. I emailed professor…
……Rotman 和 Birkhoff/MacLane 都不是开始学习代数的理想选择。有大量更温和、更现代的书。至于能在网上找到的大部头，我推荐 Shoup 的《A Computational Introduction to Number Theory and Algebra》[1]。顺便提一句，范畴论只用于编程语言研究中关于（纯）函数式编程的部分。在其他子领域（比如面向对象 OO、逻辑编程以及……
…neither Rotman nor Birkhoff/MacLane are ideal places to start learning algebra. There are plenty of gentler, more modern books. In terms of tomes that are available online, I can recommend Shoup's "A Computational Introduction to Number Theory and Algebra" [1]. As an aside, note that category theory is used only in the part of programming language research that is about (pure) functional programming. In other sub-fields (e.g. OO, logic programming and…
也许是 Victor Shoup 写的《A Computational Introduction to Number Theory and Algebra》？Dan Boneh 在他的密码学课上推荐过这本。
Perhaps "A Computational Introduction to Number Theory and Algebra" by Victor Shoup? This was recommended by Dan Boneh in his crypto course.
……至少是一个计算有限生成双曲群的 Dehn 呈现的算法，不过这看起来是个很酷的资源，包含许多有趣的主题。HN 网友可能还会喜欢 Shoup 的另一本书《a computational introduction to number theory and algebra》[0]，它的内容广泛得多，较少关注实现，但依然是一本非常有趣的书 [0]https://shoup.net/ntb/
…at least an algorithm to compute Dehn presentations of f.g. hyperbolic groups, but it looks like a cool resource with plenty of interesting topics. Another book the HN crowd might like is Shoup's "a computational introduction to number theory and algebra"[0], it is much more broad and with litte focus on implementations, but a very interesting book nonetheless [0]https://shoup.net/ntb/